Two circular loops of radii 0.05 m and 0.09m are placed such that their axes coincide and their centres are 0.12m apart. Charge of `10^(-6)C` is spread uniformly on each loop. Find the potential difference between the centres of loops.

Explanation

Distance between the two centres, `x = 0.12m`

Potential at the centre of the loop A due to charge on it,
`V_(A) = 1/(4 pi epsilon_0) (q_1)/(r_1) = (9xx10^(9)xx10^(-6))/(0.05) = 1.8 xx 10^(5)V`
Potential at the centre of the loop A due to charge on loop B,
`V_(A)^(') = 1/(4 pi epsilon_0) (q_1)/(sqrt(r_(2)^(2)+x^(2))) = (9xx10^(9)xx10^(-6))/(sqrt((0.09)^(2)+(0.12)^(2)))`
`=(9xx 10^3)/(15xx10^(-2)) = 0.6 xx 10^(5)V`
Therefore total potential at the centre of loop A,
`(V_A)_(T) = V_(A) + V_(A)^(') = (1.8 + 0.6) xx 10^(5)V = 2.4 xx 10^(5)V`
Now potential at the centre at the centre of the loop B due to charge on it,
`V_(B) = V_(A) = 1/(4 pi epsilon_0) (q_2)/(r_2) = (9xx10^(9)xx10^(-6))/(0.09) = 1 xx 10^(5)V`
Potential at the centre of the loop B due to charge on loop A,
`V_(B)^(') = 1/(4 pi epsilon_0) (q_2)/(sqrt(r_(2)^(2)+x^(2))) = (9xx10^(9)xx10^(-6))/(sqrt((0.05)^(2)+(0.12)^(2)))`
`=(9xx 10^3)/(13xx10^(-2)) = 0.69 xx 10^(5)V`
Therefore total potential at the centre of loop B,
`(V_A)_(T) = (V_(B) + V_(B)^(')) = (1 xx 10^(5)+0.69 xx 10^5)`
`= 1.69 xx 10^(5)V`
Thus potential difference,
`(V_A)_(T) - (V_B)_(T) = (2.4-1.69) xx 10^(5)V`
`= 7.1 xx 10^(4) V ~~ 72 kV`.